Saddle Point Problems And Their Iterative Solution

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Saddle-Point Problems and Their Iterative Solution

Author : Miroslav Rozložník
Publisher : Springer
ISBN 13 : 3030014312
Total Pages : 147 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Saddle-Point Problems and Their Iterative Solution by : Miroslav Rozložník

Download or read book Saddle-Point Problems and Their Iterative Solution written by Miroslav Rozložník and published by Springer. This book was released on 2018-11-19 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering. The focus is on discussing the particular properties of such linear systems, and a large selection of algebraic methods for solving them, with an emphasis on iterative methods and preconditioning. The theoretical results presented here are complemented by a case study on potential fluid flow problem in a real world-application. This book is mainly intended for students of applied mathematics and scientific computing, but also of interest for researchers and engineers working on various applications. It is assumed that the reader has completed a basic course on linear algebra and numerical mathematics.

Model Order Reduction: Theory, Research Aspects and Applications

Author : Wilhelmus H. Schilders
Publisher : Springer Science & Business Media
ISBN 13 : 3540788417
Total Pages : 471 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Model Order Reduction: Theory, Research Aspects and Applications by : Wilhelmus H. Schilders

Download or read book Model Order Reduction: Theory, Research Aspects and Applications written by Wilhelmus H. Schilders and published by Springer Science & Business Media. This book was released on 2008-08-27 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

Iterative Methods for Sparse Linear Systems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 0898715342
Total Pages : 537 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Iterative Methods for Sparse Linear Systems by : Yousef Saad

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications

Author : Daniele Bertaccini
Publisher : CRC Press
ISBN 13 : 1351649612
Total Pages : 321 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications by : Daniele Bertaccini

Download or read book Iterative Methods and Preconditioning for Large and Sparse Linear Systems with Applications written by Daniele Bertaccini and published by CRC Press. This book was released on 2018-02-19 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear systems. The solution of large and sparse linear systems is the most time-consuming part for most of the scientific computing simulations. Indeed, mathematical models become more and more accurate by including a greater volume of data, but this requires the solution of larger and harder algebraic systems. In recent years, research has focused on the efficient solution of large sparse and/or structured systems generated by the discretization of numerical models by using iterative solvers.

A Journey through the History of Numerical Linear Algebra

Author : Claude Brezinski
Publisher : SIAM
ISBN 13 : 1611977231
Total Pages : 813 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis A Journey through the History of Numerical Linear Algebra by : Claude Brezinski

Download or read book A Journey through the History of Numerical Linear Algebra written by Claude Brezinski and published by SIAM. This book was released on 2022-12-06 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: This expansive volume describes the history of numerical methods proposed for solving linear algebra problems, from antiquity to the present day. The authors focus on methods for linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of important contributors to the field. A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, people involved in scientific computing, and historians of mathematics.

Wavelet Methods — Elliptic Boundary Value Problems and Control Problems

Author : Angela Kunoth
Publisher : Springer Science & Business Media
ISBN 13 : 332280027X
Total Pages : 150 pages
Book Rating : 4.3/5 (228 download)

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Book Synopsis Wavelet Methods — Elliptic Boundary Value Problems and Control Problems by : Angela Kunoth

Download or read book Wavelet Methods — Elliptic Boundary Value Problems and Control Problems written by Angela Kunoth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diese Monographie spannt einen Bogen rund um die aktuelle Thematik Wavelets, um neueste Entwicklungen anhand aufeinander aufbauender Probleme darzustellen und das konzeptuelle Potenzial von Waveletmethoden für Partielle Differentialgleichungen zu demonstrieren.

Numerical Methods for Differential Equations, Optimization, and Technological Problems

Author : Sergey Repin
Publisher : Springer Science & Business Media
ISBN 13 : 9400752873
Total Pages : 446 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Numerical Methods for Differential Equations, Optimization, and Technological Problems by : Sergey Repin

Download or read book Numerical Methods for Differential Equations, Optimization, and Technological Problems written by Sergey Repin and published by Springer Science & Business Media. This book was released on 2012-10-13 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO 2011) held in Jyväskylä, Finland, June 9–11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmäki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmäki.

Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations

Author : Owe Axelsson
Publisher : Bentham Science Publishers
ISBN 13 : 1608052915
Total Pages : 153 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations by : Owe Axelsson

Download or read book Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations written by Owe Axelsson and published by Bentham Science Publishers. This book was released on 2011 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. M

Algorithms for Sparse Linear Systems

Author : Jennifer Scott
Publisher : Springer Nature
ISBN 13 : 3031258207
Total Pages : 254 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Algorithms for Sparse Linear Systems by : Jennifer Scott

Download or read book Algorithms for Sparse Linear Systems written by Jennifer Scott and published by Springer Nature. This book was released on 2023-04-29 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines. This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964793
Total Pages : 995 pages
Book Rating : 4.4/5 (649 download)

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Book Synopsis Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition by :

Download or read book Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 995 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Finite Elements and Fast Iterative Solvers

Author : Howard Elman
Publisher : OUP Oxford
ISBN 13 : 0191667927
Total Pages : 495 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Finite Elements and Fast Iterative Solvers by : Howard Elman

Download or read book Finite Elements and Fast Iterative Solvers written by Howard Elman and published by OUP Oxford. This book was released on 2014-06-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

Domain Decomposition Methods 10

Author : Jan Mandel
Publisher : American Mathematical Soc.
ISBN 13 : 0821809881
Total Pages : 569 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Domain Decomposition Methods 10 by : Jan Mandel

Download or read book Domain Decomposition Methods 10 written by Jan Mandel and published by American Mathematical Soc.. This book was released on 1998 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Tenth International Conference on Domain Decomposition Methods, which focused on the latest developments in realistic applications in structural mechanics, structural dynamics, computational fluid dynamics, and heat transfer. The proceedings of these conferences have become standard references in the field and contain seminal papers as well as the latest theoretical results and reports on practical applications.

Discretization Methods and Iterative Solvers Based on Domain Decomposition

Author : Barbara I. Wohlmuth
Publisher : Springer Science & Business Media
ISBN 13 : 3642567673
Total Pages : 209 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Discretization Methods and Iterative Solvers Based on Domain Decomposition by : Barbara I. Wohlmuth

Download or read book Discretization Methods and Iterative Solvers Based on Domain Decomposition written by Barbara I. Wohlmuth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

The Art and Science of Machine Intelligence

Author : Walker H. Land Jr.
Publisher : Springer
ISBN 13 : 303018496X
Total Pages : 284 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Art and Science of Machine Intelligence by : Walker H. Land Jr.

Download or read book The Art and Science of Machine Intelligence written by Walker H. Land Jr. and published by Springer. This book was released on 2019-06-25 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents several machine intelligence technologies, developed over recent decades, and illustrates how they can be combined in application. One application, the detection of dementia from patterns in speech, is used throughout to illustrate these combinations. This application is a classic stationary pattern detection task, so readers may easily see how these combinations can be applied to other similar tasks. The expositions of the methods are supported by the basic theory they rest upon, and their application is clearly illustrated. The book’s goal is to allow readers to select one or more of these methods to quickly apply to their own tasks. Includes a variety of machine intelligent technologies and illustrates how they can work together Shows evolutionary feature subset selection combined with support vector machines and multiple classifiers combined Includes a running case study on intelligent processing relating to Alzheimer’s / dementia detection, in addition to several applications of the machine hybrid algorithms

Iterative Optimization in Inverse Problems

Author : Charles Byrne
Publisher : CRC Press
ISBN 13 : 1482222345
Total Pages : 298 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Iterative Optimization in Inverse Problems by : Charles Byrne

Download or read book Iterative Optimization in Inverse Problems written by Charles Byrne and published by CRC Press. This book was released on 2014-02-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author's considerable research in the field, including his recently developed class of SUMMA algorithms

Acta Numerica 2005: Volume 14

Author : Arieh Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521858076
Total Pages : 584 pages
Book Rating : 4.8/5 (58 download)

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Book Synopsis Acta Numerica 2005: Volume 14 by : Arieh Iserles

Download or read book Acta Numerica 2005: Volume 14 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2005-06-30 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact factor, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.

Determining input-output properties of linear time-invariant systems from data

Author : Anne Koch
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832554467
Total Pages : 151 pages
Book Rating : 4.8/5 (325 download)

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Book Synopsis Determining input-output properties of linear time-invariant systems from data by : Anne Koch

Download or read book Determining input-output properties of linear time-invariant systems from data written by Anne Koch and published by Logos Verlag Berlin GmbH. This book was released on 2022-02-08 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to their relevance in systems analysis and controller design, this thesis considers the problem of determining input-output properties of linear time-invariant systems. While obtaining a suitable mathematical model describing the input-output behavior of a dynamical system can be a difficult task, data of the system in form of input-output trajectories is often and increasingly available. This thesis therefore introduces three complementary data-driven analysis methods to determine input-output properties directly from data without deriving a mathematical model first. In particular, the results of this thesis include iterative methods, where data is actively sampled by performing experiments on the unknown system, as well as approaches based on available (offline) data. All these approaches are simple to apply, come with low requirements on the data, and provide rigorous theoretical guarantees. Systems analysis not only provides insights into the system and allows to do controller design with guaranteed stability, but it can also validate a given controller or its closed-loop performance. By developing different methods to determine input-output properties directly from data on the basis of a rigorous mathematical analysis, this thesis contributes to a sound mathematical framework for data-driven systems analysis and control theory.